Short answers, pulled from the story.
The Battle of Chateau-Thierry was fought on the 12th of February 1814. It was part of the Six Days' Campaign, a series of French victories over Blucher's Army of Silesia during the broader War of the Sixth Coalition.
The Allied forces were led by Prussian General Ludwig Yorck von Wartenburg and Russian General Fabian Wilhelm von Osten-Sacken. Both corps were retreating after being defeated at the Battle of Montmirail the previous day.
Historians Chandler and Petre recorded 1,250 Prussian casualties, 1,500 Russian casualties, and 600 French. The French also captured nine cannons and significant baggage. Other sources place French losses at 400-600 and Russian losses at 1,200-1,500.
Napoleon failed primarily because Marshal MacDonald barely moved and did not capture the Chateau-Thierry bridge over the Marne in time. The Allied rear guard held long enough for most troops to cross before the bridge was destroyed, and a Prussian 12-pounder battery on the north bank prevented French pursuit.
Major Stockhausen's two East Prussian battalions formed the final rear guard inside Chateau-Thierry. They fought long enough to allow other units to cross the Marne, but when his 400 survivors reached the bridge, it had already been destroyed. They were compelled to surrender.
Chateau-Thierry was the third action of the Six Days' Campaign. It followed the destruction of Olsufiev's corps at Champaubert on the 10th of February and the hard-fought Battle of Montmirail on the 11th. Two days later, on the 14th of February, Napoleon fought the Battle of Vauchamps against Blucher's remaining corps.